Question: Graph this system of equations and solve. $-16x-8y = -40$ $4x-8y = 40$ 1 2 3 4 5 6 7 8 9 10 \llap{-}2 \llap{-}3 \llap{-}4 \llap{-}5 \llap{-}6 \llap{-}7 \llap{-}8 \llap{-}9 \llap{-}10 1 2 3 4 5 6 7 8 9 10 \llap{-}2 \llap{-}3 \llap{-}4 \llap{-}5 \llap{-}6 \llap{-}7 \llap{-}8 \llap{-}9 \llap{-}10 Click and drag the points to move the lines.
Explanation: Convert the first equation, $-16x-8y = -40$ , to slope-intercept form. $y = -2 x + 5$ The y-intercept for the first equation is $5$ , so the first line must pass through the point $(0, 5)$ The slope for the first equation is $-2$ . Remember that the slope tells you rise over run. So in this case for every $2$ positions you move down (because it's negative) $1$ position to the right. $2$ positions down from $(0, 5)$ is $(1, 3)$ Graph the blue line so it passes through $(0, 5)$ and $(1, 3)$ Convert the second equation, $4x-8y = 40$ , to slope-intercept form. $y = \dfrac{1}{2} x - 5$ The y-intercept for the second equation is $-5$ , so the second line must pass through the point $(0, -5)$ The slope for the second equation is $\dfrac{1}{2}$ . Remember that the slope tells you rise over run. So in this case for every $1$ position you move up You must also move $2$ position to the right. $2$ positions to the right. Graph the green line so it passes through $(0, -5)$ and $(2, -4)$ The solution is the point where the two lines intersect. The lines intersect at $(4, -3)$.